The 33-year-old says that he had already "started negotiating" with the Premier League outfit, but AC Milan, for whom he was playing at the time, stopped the transfer.
"Actually, Milan wouldn't let me go," Pirlo told the Daily Mail. "I have a very strong connection with Ancelotti, so I was in touch with him when he went to Chelsea, and I'm still in touch with him now he's at Paris Saint-Germain.
"I had already started negotiating with the people at Chelsea but then finally Milan didn't let me go. That's why I stayed.
"Certainly it would have been a different experience that I'd have liked, especially when I was 30 years old. So why not? But unfortunately it didn't happen."
Juventus will host Chelsea in the Champions League on Tuesday.